MCQ
The circle x2 + y2 + 2gx + 2fy + c = 0 does not intersect x-axis, if:
- Ag2 < c
- Bg2 > c
- Cg2 > 2c
- DNone of these
Solution:
Given:
x2 + y2 + 2gx + 2fy + c = 0 ......... (1)
The given circle intersects the x-axis.
The equation of circle becomes x2 + 2gx + c = 0 ......... (2)
Solving equation (2):
$\therefore$ Discriminant, $\text{D}=\sqrt{4\text{g}^2-4\text{c}}\geq0$
$\Rightarrow4\text{g}^2-4\text{c}\geq0$
$\Rightarrow\text{g}^2-\text{c}\geq0$
$\Rightarrow\text{g}^2\geq\text{c}$
Hence, if g2 < c, then the given circle will not intersect the x-axis.
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